Physics 1-08 Vector Addition
Name: _________________
Vectors
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Vectors are measurements with __________________ and _______________.
o They are represented by _______________.
o The length of the arrow is the ___________________.
o The direction of the arrow is the ____________________.
Can be represented in ________________________ form
o Make a _____________________ using the vector as the __________________
o Use ______________ and ___________________ to find the horizontal (x) component and the
vertical (y) component
o Assign ____________________ signs to any component going ____________ or ___________
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sin(𝜃) =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
cos(𝜃) =
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
tan(𝜃) =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
A football player kicks a ball at 15 m/s at 30° above the ground. Find the horizontal and vertical components
of this velocity.
Scalar Multiplication
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Multiplying a vector by a _________________ number
Draw the vector that many times in a __________________
Or multiply the _________________________ by that number
A negative vector means multiply by -1, so it goes in the ________________________ direction
Vector Addition - Graphical Method
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Draw the __________________ vector.
Draw the second vector where the ______________________________ (tip-to-tail).
Draw the resultant vector from where the _____________ vector begins to where the
________________ vector ends.
________________________ the resultant's length and direction.
Vector Addition - Component Method
Vectors can be described by its
___________________ to show how far
it goes in the x and y directions.
To add vectors, you simply add
the ________________________ and
______________________ to get total
(________________________) x and y
components.
1. Find the
_________________________
for __________ the vectors
to be added
2. _______________ all the ______ components
3. _______________ all the ______ components
4. Use the _________________________ Theorem to find the _____________________ of the resultant
5. Use ____________ to find the ______________________ (the direction is always found at the __________________ of the resultant)
Note: Drawing pictures and triangles helps immensely.
Add the following vectors. 𝑪 = 15 𝑚 at 25° N of E; 𝑫 = 20 𝑚 at 60° S of E
Created by Richard Wright – Andrews Academy
To be used with OpenStax High School Physics
Physics 1-08 Vector Addition
Name: _________________
A jogger runs 145 m in the direction 20.0° east of north and then 105 m in a direction 35.0° south of east. Determine the magnitude and
direction of jogger's position from her starting point.
Practice Work
1.
(a) Is it possible for one component of a vector to be zero, while the vector itself is not zero? (b) Is it possible for a vector to be zero,
while one component is not zero? Explain.
2.
Can two nonzero perpendicular vectors be added together so their sum is zero? Explain.
3.
Can three or more vectors with unequal magnitudes be added together so their sum is zero? If so, show by means of a tip-to-tail
arrangement of the vectors how this could occur.
4.
An ostrich is running at a speed of 17.0 m/s in a direction of 68.0° north of west. What is the magnitude of ostrich's velocity component
that is directed (a) due north and (b) due west? (RW) 15.8 m/s, 6.37 m/s
5.
An ocean liner leaves New York City and travels 18.0° north of east for 155 km. How far east
and how far north has it gone? In other words, what are the magnitudes of the components of
the ship's displacement vector in the directions (a) due east and (b) due north? (Cutnell 1.33)
147 km, 47.9 km
6.
A new landowner has a triangular piece of flat land she wishes to fence. Starting at the west
corner, she measures the first side to be 80.0 m long and the next to be 105 m. These sides are
represented as displacement vectors A and B in Figure 3.61. She then correctly calculates the
length and orientation of the third side C. What is her result? (Hint: Since A + B + C = 0, then A +
B = −C.) (OpenStax 3.20) 92.3 m at 53.7° S of W
7.
Suppose you first walk 12.0 m in a direction 20° west of north and then 20.0 m in a direction
40.0° south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point
to your final position? (OpenStax 3.5) 19.5 m at 4.65° S of W
8.
A golfer, putting on a green, requires three strokes to "hole the ball." During the first putt, the ball rolls 5.0 m due east. For the second
putt, the ball travels 2.1 m at an angle of 20.0° north of east. The third putt is 0.50 m due north. What displacement (magnitude and
direction relative to due east) would have been needed to "hole the ball" on the very first putt? (Cutnell 1.41) 7.1 m at 9.9° N of E
9.
You are on a treasure hunt and your map says, "Walk due west for 52 paces, then walk 30.0° north of west for 42 paces, and finally walk
due north for 25 paces." What is the magnitude of the component of your displacement (a) due north and (b) due west? (Cutnell 1.42)
46 paces, 88 paces
10. On a safari, a team of naturalists sets out toward a research station located 4.8 km away in a direction 42° north of east. After traveling
in a straight line for 2.4 km, they stop and discover that they have been traveling 22° north of east, because their guide misread his
compass. What are (a) the magnitude and (b) the direction (relative to due east) of the displacement vector now required to bring the
team to the research station? (Cutnell 1.45) 2.7 km at 60° N of E
11. While snorkeling in the ocean, you swim directly towards shore at 2 m/s. The current of the water pushes you directly sideways at 3
m/s. What is your resultant velocity (magnitude and direction relative to your intended path of straight towards shore)? (RW) 3.6 m/s
at 56.3°
12. An airplane flies at 200 km/h at 30.0° N of W. The wind blows it at 30 km/h at 45.0° E of N. What is the resultant velocity of the airplane
(magnitude and direction)? (RW) 194 km/h at 38.6° N of W
13. You are trying to row a boat directly across a river that is 50.0 m wide. You can row at 3.1 m/s in a direction directly across the river
perpendicular to the shore. The current is 4.8 m/s parallel to shore. (a) What is your velocity relative to the shore? (b) How much time
does it take to get to the other side of the river? (c) How far downstream do you land? (RW) 5.71 m/s at 32.9° downstream from
shore, 16.1 s, 77.4 m
Created by Richard Wright – Andrews Academy
To be used with OpenStax High School Physics